What it would mean if the iPad gets a "retina display"

Lots of rumblings about the 2nd gen iPad that's due to be announced in a month or two, along with talk of whether or not it will follow in the iPhone 4's footsteps by gaining a "retina display". Some insane numbers are being thrown around, as evidence of its impossibility, but the insanity of these numbers is due to a lot of people assuming that "retina display" means "over 300 pixels per inch, linear resolution", which is a mistake.

In announcing the retina display at the WWDC 2010 keynote, Steve Jobs didn't just say "300 is magic", without qualifiers. The full quote is:

"It turns out that there's a magic number right around 300 pixels per inch, that when you hold something around 10 or 12 inches away from your eyes, is the limit of the human retina to differentiate the pixels."

(apologies for the grammar, but that's the exact quote.)

Which, as this in-depth examination shows, is a quite accurate statement for 20/20 vision. Steve made a big deal about the 300 thing, but that only applies if you're holding it at 10-12 inches from your eye.

BUT: You simply cannot comfortably use the iPad at ten inches from your eye. It's too big for that. I can see 14 inches being a comfortable distance, though.

Now, applying the same assumptions and simple bit of trig as used at that link, we find that to meet the "retina display" criterion at some greater distances, we'd need:

1/(13*tan(1 arc minute)) ~= 264 ppi
1/(14*tan(1 arc minute)) ~= 246 ppi

Oh ho! 264 ppi corresponds exactly to a doubling of existing iPad resolution, to 2048 by 1536. That meets the standard of "retina display" at 13 inches from your eye.

Another common size, 1920 by 1440, would give the iPad display a density of 247 ppi. Which is perfect for "retina display" at 14 inches. Slightly more achievable, perhaps, but lacking that nice 2x scaling factor.

I'd say both of these resolutions ARE within the capabilities of modern hardware. No, you're not going to be running the latest cutting-edge FPS at that resolution, but videos and standard graphics? No problem.

The iPhone 4 can play H.264 1080p videos perfectly without breaking a sweat, and it doesn't even officially support that. The CPU/GPU in the new iPad will have another years' worth of R&D on top of that.

Now, whether or not they can make a 9 or 10 inch display of that resolution and still meet their price points is quite another matter.

For reference: a 1.5x (1536 by 1152; 198 ppi) display would meet "retina" criteria at 17-18 inches from the eye, which is roughly the distance from eye to screen if you're a moderately tall adult and it's sitting in your lap or on the table in front of you, but it would lose it's, umm, retina magic if you held it any closer than that. (Assuming, of course, you have 20/20 vision.)